Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems

  • F. Battelli
  • K. J. Palmer


We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic center manifolds. We assume that the unperturbed system has an orbit that connects a hyperbolic fixed point on one center manifold to a hyperbolic fixed point on the other. Then we prove some old and new results concerning the persistence of these connecting orbits and apply the results to find examples of systems in dimensions greater than three that possess Sil’nikov saddle-focus homoclinic orbits.


Tangent Space Invariant Manifold Unstable Manifold Homoclinic Orbit Stable Manifold 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • F. Battelli
    • 1
  • K. J. Palmer
    • 2
  1. 1.Marche Polytechnic UniversityAnconaItaly
  2. 2.National Taiwan UniversityTaipeiTaiwan

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